Abstract
AbstractIn this paper, we address optimal control problems subject to fluid flows through poro-visco-elastic media. In particular, we focus on the case of given permeability k(x, t), which translates into a convex control problem, with both distributed and boundary controls. We focus on investigating the problem of maintaining the solid displacement and Darcy pressure close to desired values (motivated by applications related to tissue perfusion in the eye and its relationship to the development of glaucoma) using the sources present in the system as control variables. The results provided in this paper include existence and uniqueness of optimal control, as well as the characterization of the optimal control through the first order necessary optimality conditions, based on the adjoint system.
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